Wave-particle duality and `bipartite' wave functions for a single particle

Details Wave-particle duality and `bipartite' wave functions for a single particle Wave-particle duality and `bipartite' wave functions for a single particle

2006-09-12

arxiv.org/abs/quant-ph/0609092v1

Physics

Quantum Physics

3 pages

Scientific paper

It is shown that `bipartite' wave functions can present a mathematical formalism of quantum theory for a single particle, in which the associated Schr\"{o}dinger's wave functions correspond to those `bipartite' wave functions of product forms. This extension of Schr\"{o}dinger's form establishes a mathematical expression of wave-particle duality and that von Neumann's entropy is a quantitative measure of complementarity between wave-like and particle-like behaviors. In particular, this formalism suggests that collapses of Schr\"{o}dinger's wave functions can be regarded as the simultaneous transition of the particle from many levels to one. Our results shed considerable light on the basis of quantum mechanics, including quantum measurement.

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